Question: Solve for $x$ and $y$ using elimination. ${-x-6y = -45}$ ${x-5y = -21}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-11y = -66$ $\dfrac{-11y}{{-11}} = \dfrac{-66}{{-11}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x-6y = -45}\thinspace$ to find $x$ ${-x - 6}{(6)}{= -45}$ $-x-36 = -45$ $-x-36{+36} = -45{+36}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {x-5y = -21}\thinspace$ and get the same answer for $x$ : ${x - 5}{(6)}{= -21}$ ${x = 9}$